Sigref – A Symbolic Bisimulation Tool Box

  • Ralf Wimmer
  • Marc Herbstritt
  • Holger Hermanns
  • Kelley Strampp
  • Bernd Becker
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4218)


We present a uniform signature-based approach to compute the most popular bisimulations. Our approach is implemented symbolically using BDDs, which enables the handling of very large transition systems. Signatures for the bisimulations are built up from a few generic building blocks, which naturally correspond to efficient BDD operations. Thus, the definition of an appropriate signature is the key for a rapid development of algorithms for other types of bisimulation.

We provide experimental evidence of the viability of this approach by presenting computational results for many bisimulations on real-world instances. The experiments show cases where our framework can handle state spaces efficiently that are far too large to handle for any tool that requires an explicit state space description.


Label Transition System Binary Decision Diagram Block Number Symbolic Model Check Current Partition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Wimmer, R., Herbstritt, M., Becker, B.: Minimization of Large State Spaces using Symbolic Branching Bisimulation. In: Proc. of IEEE Workshop on Design & Diagnostics of Electronic Circuits & Systems (DDECS), pp. 9–14 (2006)Google Scholar
  2. 2.
    Chehaibar, G., et al.: Specification and Verification of the PowerScaleTM Bus Arbitration Protocol: An Industrial Experiment with LOTOS. In: Proc. of FORTE, vol. 69, pp. 435–450 (1996)Google Scholar
  3. 3.
    Giannakopoulou, D.: Model Checking for Concurrent Software Architectures. PhD thesis, Imperial College, University of London (1999)Google Scholar
  4. 4.
    Graf, S., Steffen, B., Luttgen, G.: Compositional minimisation of finite state systems using interface specifications. Formal Asp. of Comp. 8(5), 607–616 (1996)MATHCrossRefGoogle Scholar
  5. 5.
    Kanellakis, P., Smolka, S.: CCS expressions, finite state processes, and three problems of equivalence. Information and Computation 86(1), 43–68 (1990)MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM Jour. on Computing 16(6), 973–989 (1987)MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Burch, J., et al.: Symbolic Model Checking: 1020 States and Beyond. Information and Computation 98(2), 142–170 (1992)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Bouajjani, A., Fernandez, J.C., Halbwachs, N.: Minimal model generation. In: Clarke, E., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 197–203. Springer, Heidelberg (1991)CrossRefGoogle Scholar
  9. 9.
    Bouajjani, A., Fernandez, J.C., Halbwachs, N., Ratel, C., Raymond, P.: Minimal state graph generation. Science of Computer Programming 18, 247–269 (1992)MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Bouali, A., de Simone, R.: Symbolic Bisimulation Minimisation. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 96–108. Springer, Heidelberg (1993)Google Scholar
  11. 11.
    Blom, S., Orzan, S.: Distributed Branching Bisimulation Reduction of State Spaces. ENTCS 89(1), 113–990 (2003)Google Scholar
  12. 12.
    Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)MATHGoogle Scholar
  13. 13.
    Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)Google Scholar
  14. 14.
    Milner, R.: Lectures on a Calculus for Communicating Systems. In: Brookes, S.D., Winskel, G., Roscoe, A.W. (eds.) Seminar on Concurrency. LNCS, vol. 197, pp. 197–220. Springer, Heidelberg (1985)Google Scholar
  15. 15.
    van Glabbeek, R., Weijland, W.: Branching Time and Abstraction in Bisimulation Semantics. Journal of the ACM 43(3), 555–600 (1996)CrossRefMathSciNetMATHGoogle Scholar
  16. 16.
    Baeten, J., van Glabbeek, R.: Another Look at Abstraction in Process Algebra. In: Ottmann, T. (ed.) ICALP 1987. LNCS, vol. 267, pp. 84–94. Springer, Heidelberg (1987)Google Scholar
  17. 17.
    Bergstra, J.A., Ponse, A., van der Zwaag, M.B.: Branching time and orthogonal bisimulation equivalence. Theor. Comp. Sci. 309, 313–355 (2003)MATHCrossRefGoogle Scholar
  18. 18.
    Milner, R.: A Modal Characterization of Observable Machine-Behaviour. In: Astesiano, E., Böhm, C. (eds.) CAAP 1981. LNCS, vol. 112, pp. 25–34. Springer, Heidelberg (1981)Google Scholar
  19. 19.
    Montanari, U., Sassone, V.: Dynamic congruence vs. progressing bisimulation for CCS. Fundam. Inform. 16(1), 171–199 (1992)MATHMathSciNetGoogle Scholar
  20. 20.
    Bouajjani, A., et al.: Safety for Branching Time Semantics. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510, pp. 76–92. Springer, Heidelberg (1991)Google Scholar
  21. 21.
    van Glabbeek, R.J.: The linear time – branching time spectrum II. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 66–81. Springer, Heidelberg (1993)Google Scholar
  22. 22.
    Hermanns, H., Lohrey, M.: Priority and maximal progress are completely axiomatisable. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 237–252. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  23. 23.
    Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)CrossRefGoogle Scholar
  24. 24.
    Dovier, A., Gentilini, R., Piazza, C., Policriti, A.: Rank-based symbolic bisimulation (and model checking). ENTCS 67 (2002)Google Scholar
  25. 25.
    Klarlund, N.: An nlogn algorithm for online BDD refinement. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 107–118. Springer, Heidelberg (1997)Google Scholar
  26. 26.
    Somenzi, F.: CUDD: CU Decision Diagram Package Release 2.4.1. University of Colorado at Boulder (2005)Google Scholar
  27. 27.
    Groote, J.F., Vaandrager, F.W.: An Efficient Algorithm for Branching Bisimulation and Stuttering Equivalence. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 626–638. Springer, Heidelberg (1990)CrossRefGoogle Scholar
  28. 28.
    Bryant, R.: Graph-Based Algorithms for Boolean Function Manipulation. IEEE Trans. on Comp. 35(8), 677–691 (1986)MATHCrossRefGoogle Scholar
  29. 29.
    Wegener, I.: Branching programs and binary decision diagrams. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia (2000)MATHCrossRefGoogle Scholar
  30. 30.
    Strampp, K.: Symbolische Berechnung von Bisimulationen. Diploma thesis, Albert-Ludwigs-University Freiburg, Germany (2006)Google Scholar
  31. 31.
    Matsunaga, Y., McGeer, P.C., Brayton, R.K.: On computing the transitive closure of a state transition relation. In: Proc. of DAC, pp. 260–265. ACM Press, New York (1993)Google Scholar
  32. 32.
    Burch, J.R., et al.: Sequential circuit verification using symbolic model checking. In: Proc. of DAC, pp. 46–51. ACM Press, New York (1990)Google Scholar
  33. 33.
    Garavel, H., Hermanns, H.: On Combining Functional Verification and Performance Evaluation using CADP. In: Eriksson, L.-H., Lindsay, P.A. (eds.) FME 2002. LNCS, vol. 2391, Springer, Heidelberg (2002)CrossRefGoogle Scholar
  34. 34.
    Fernandez, J.C., et al.: CADP: A Protocol Validation and Verification Toolbox. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 437–440. Springer, Heidelberg (1996)Google Scholar
  35. 35.
    Herbstritt, M., Wimmer, R., Peikenkamp, T., Böde, E., Adelaide, M., Johr, S., Hermanns, H., Becker, B.: Analysis of Large Safety-Critical Systems: A quantitative Approach. Reports of SFB/TR 14 AVACS 8 (2006) ISSN 1860-9821Google Scholar
  36. 36.
    Ciardo, G., Tilgner, M.: On the use of Kronecker operators for the solution of generalized stochastic Petri nets. Technical Report 96-35, ICASE (1996)Google Scholar
  37. 37.
    Kuntz, M., Siegle, M., Werner, E.: Symbolic Performance and Dependability Evaluation with the Tool CASPA. In: Núñez, M., Maamar, Z., Pelayo, F.L., Pousttchi, K., Rubio, F. (eds.) FORTE 2004. LNCS, vol. 3236, pp. 293–307. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  38. 38.
    Harel, D., Politi, M.: Modelling Reactive Systems with Statecharts: The Statemate Approach. McGraw-Hill, New York (1998)Google Scholar
  39. 39.
    ERTMS: Project (May 16, 2006), Website
  40. 40.
    ARP 4761: Guidelines and Methods for Conducting the Safety Assessment Process on Civil Airborne Systems and Equipment. Aerospace Recommended Practice, Society of Automotive Engineers, Detroit, USA (1996)Google Scholar
  41. 41.
    Hermanns, H.: Interactive Markov Chains: The Quest for Quantified Quality. In: Hermanns, H. (ed.) Interactive Markov Chains. LNCS, vol. 2428, Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Ralf Wimmer
    • 1
  • Marc Herbstritt
    • 1
  • Holger Hermanns
    • 2
  • Kelley Strampp
    • 1
  • Bernd Becker
    • 1
  1. 1.Albert-Ludwigs-University FreiburgGermany
  2. 2.Saarland UniversitySaarbrückenGermany

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